Question

Mass of $2\, kg$ is moving with a string in horizontal circle with angular velocity $5$ cycles/min keeping the radius constant, tension in string is doubled. Now, the angular velocity of the mass will be

• A. 14 cycles/min
• B. 10 cycles/min
• C. 2.25 cycles/min
• D. 7 cycles/min

Answer 1

Answer: (D)

Tension in the string should be equal to centripetal force
$T=\frac{m v^{2}}{r}$
where, $m=$ mass of body
$r=$ radius of circular path
$v=$ linear velocity of body
$m$ and $r$ are constant.
Hence, $v \propto \sqrt{T}$
$\therefore \frac{v_{2}}{v_{1}}=\left(\frac{T_{2}}{T_{1}}\right)^{1 / 2}=\left(\frac{2 T_{1}}{T_{1}}\right)^{1 / 2} $
$v_{2}=\sqrt{2} v_{1}=\sqrt{2} \times 5 $
$=5 \times 1.4=7$ cycles/min